Redistricting-plank-Compactness
A paper from 2011 on measuring compactness for purposes of legislative redistricting is publicly posted here: * A Single Compactness Measure for Legislative Redistricting http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1857944 Some of the paper is highly mathematical (the proof that an entire class of compactness measures ranks any two redistricting plans exactly the same). However, most of the paper is very understandable, especially the counterexamples showing why most of the proposed measures of compactness can be used for gerrymandering because they do not reliably measure compactness. Abstract: Legislative districts in the 50 states are being redrawn following the completion of the 2010 United States census. Thirty-five states require that districts are compact, which is believed to make gerrymandering - designing legislative districts so as to advantage one political party - more difficult. There are now more than a dozen proposed competing numerical measures of the relative compactness of legislative districts. This article demonstrates that nine of the proposed measures of compactness do not reliably measure compactness. Pictorial counterexamples show that these nine proposed measures of area compactness assign the exact same value to shapes having visually distinct compactness levels. Next, this paper mathematically proves that all area-to-perimeter or area to square-of-perimeter measures (or their reciprocals or square roots) rank the compactness of any two sets of redistricting plans in the exact same order. Thus, these reliable proposed measures of district compactness are equivalent to the simplest such measure defined as the ratio of area to the square of the perimeter. An index of compactness is conceptually and computationally best when it has a maximum value of one (1) when the area is as compact as a circle, a minimum value approaching zero when the area's perimeter is very large compared to its area, and provides a direct comparison of any two districts' compactness regardless of district area size. This compactness measure is 4π times the ratio of the area of the district to the square-of-its-perimeter, known in mathematics as the isoperimetric quotient. This paper concludes by briefly setting the general context within which a compactness measure is applied to compare proposed district plans meeting other crucial considerations. Excerpt: The Legislative Redistricting Context of Compactness Measures In drawing district maps, compactness only comes into play after other considerations are met. 'Communities of interest' should be preserved as much as possible and "neighborhoods mean a lot in redistricting ... neighborhoods which would probably not pass a compactness test. Our streets are said to follow the windings of cow paths and our neighborhoods are fairly unruly in shape."5 A state district map should be chosen that: (i) has equal population districts to within 0.5%; (ii) utilizes natural and geographic boundaries and barriers such as vehicular impassable mountain ranges and rivers in the creation of district boundaries; and (iii) utilizes existing neighborhood, municipal and county government boundaries in the creation of district boundaries.6 One possible procedure for redistricting, might be to allow various parties to propose district maps that meet the above three conditions, and the "winning" map would be one that has a minimum sum of compactness of districts, and has a minimum ratio of the number of uniquely administered districts to the number of election jurisdictions (to keep election administrative simple). These last two conditions could be equally weighted. Such a process for deciding on which district map to adopt might reduce the need for subjective judgments or competing claims and create districts that better serve voters and are easier for representatives to serve and for election officials to administer. Details * Email exchange of Sat Jun 4, 2011 on the email discussion list LWVTopics@yahoogroups.com. The quote is by Hollie Courage, former President of the League of Women Voters of Rhode Island (LWV, RI). Barbara Klein of the LWV, Arizona reminded me during the same conversation of the need to preserve 'communities of interest'. Please see http://www.lwvri.org/redistricting.htm and "The Law and Drawing District Lines" http://www.lwvri.org/law-drawingdistrictlines.htm * Some of the language in (ii) and (iii) is borrowed from Roz McGee, a Utah House member who made a different redistricting proposal in the 2007 Utah legislative session. Category:Planks from elsewhere